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AHSANULLAH UNIVERSITY OF SCIENCE & TECHNOLOGY
COURSE NO:CE-416 COURSE NAME: PRE-STRESSED CONCRETE SESSIONAL.COURSE TEACHER: GALIB MUKTADIR & SABREENA NASRIN
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Presented by-Md. Nasim AnjumID:08.01.03.106Dept. of Civil Engineering Ahsanullah University of Science & Technology
Influence Line of Reaction for Determinate Structure Due to
Moving Load
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DEFINITION An influence line is a diagram whose ordinates, which are plotted as a function of distance along the span, give the value of an internal force, a reaction, or a displacement at a particular point in a structure as a unit load move across the structure.
Variation of Reaction, shear & Moment at a specific point on a structure as a concentrated load (one unit) moves over the structure.
NOTE: Influence lines for statically determinate structures are always piecewise linear.
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Qualitative Influence Lines
“If any deforming function – stress, shear, moment or reaction is allowed to act through a very small unit displacement the resulting shape of the deflected structure will be an influence line for that function” (T. C. Shedd and J. Vawter.)
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Influence lines are used to determine where to determine for maximum result & to compute the resulting magnitude of the reaction or other actions once the loads are placed in their critical position.
For instance, when loads pass over a structure, say a bridge, one needs to know when the maximum values of shear/reaction/bending-moment will occur at a point so that the section may be designed.
Why do we need the influence lines?
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Muller-Breslau Principle The influence line for a response function is given by the deflected shape of the released structure due to a unit displacement (or rotation) at the location and in the direction of the response function.
A released structure is obtained by removing the displacement constraint corresponding to the response function of interest from the original structure.
CAUTION: Principle is only valid for force response functions. Releases:Support reaction - remove translational support restraint.Internal shear - introduce an internal glide support to allow differential displacement movement.Bending moment - introduce an internal hinge to allow differential rotation movement.
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Structure Subjected to a variable position loads.
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Influence lines for Reaction As an example, an influence line for the left reaction of a beam can be generated by placing a unit vertical displacement at the reaction point, in the direction of that reaction.
B
1
A
L
By the same method, an influence line for the reaction at B can be found by simply distorting the reaction at B upwards a unit distortion & form its own Influence Line
δy = 1 A B
Ay By
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Variation of Reaction RA & RB
as function of load position.
Moving Concentrated Load
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RA occurs only at A; RB occurs only at B
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EXAMPLE Determine the maximum reaction at support B on the beam shown due to a single
concentrate live load of 8000 N, a uniform live load of 3000 N/m, a beam weight (dead load) of 1000 N/m.
4 m 4 m 4 m
= 48000 N = 48 KN
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THANK YOU